Trump will explain tariffs on electronics on Monday

White House press secretary Karoline Leavitt was asked during Tuesday's briefing if President Trump is operating on any specific timeline for when he wants to complete negotiations on tariffs.

"Well, we always move at Trump speed here at the White House, which is incredibly fast," she responded.

Leavitt added, "the president likes to get things done, but he's very much focused on ensuring that these deals are good for the American worker, they are good for American manufacturing, and again, that they tackle these crippling deficits with these countries."

They will be "tailor-made deals," Leavitt said, with Trump directing his entire trade team to be involved in the effort.

Stocks in Europe and Asia partially rebounded Tuesday, buoyed by signals from the White House that it is open to talks on tariffs with countries.

The UK’s FTSE, Germany’s DAX and the pan-European Stoxx 600 closed at 2.5% or above.

In Asia, Japan’s Nikkei jumped over 6%, while China’s Shanghai Composite index closed at 1.4%.

However, analysts warn further volatility is likely, with Trump’s higher-rate tariffs due to go into effect Wednesday and the EU also preparing to impose its own retaliatory tariffs.

The EU reportedly plans to impose import duties of up to 25% on a range of US goods, including diamonds, motorbikes, luxury boats, domestic appliances, tobacco, poultry and many other agricultural products.

-ABC News' Patrick Reevell

Republican senators on the Senate Finance Committee admonished U.S. Trade Representative Jamieson Greer over President Donald Trump's position against offering exemptions to his sweeping tariffs.

"I'm somewhat disappointed to hear that exclusions of some of these things are-- are being ruled out at this point in time," said Wisconsin Sen. Ron Johnson.

"They're very specific situations that I think you ought to consider exclusions for because, I don't often agree with the members on the other side of the aisle, but in many cases here today, particularly when they're expressing concern about small businesses in their states, I'm hoping ... you and the president are very sensitive about companies potentially going bankrupt by these actions," Johnson continued.

Sen. Thom Tillis, a North Carolina Republican, also largely focused his questions on exemptions.

"Whose throat do I get to choke if this proves to be wrong?" Tillis asked Greer about the sweeping tariffs "alla prima" approach.

"Well, senator, you can certainly always talk to me," Greer said.

-ABC News' Fritz Farrow

Sen. Mark Warner, a Virginia Democrat, said at the Senate Finance Committee hearing with U.S. Trade Representative Jamieson Greer that an unnamed Wall Street executive he spoke to described the market situation on Tuesday as "a good day in hospice."

U.S. stocks rose at opening after days of tumbling, a recouping some losses as the Trump administration says it is beginning to negotiate tariffs with some nations.